Find the average power involved in this expansion when the engine is running at 4000 rpm, assuming that the gauge pressure immediately after combustion is 15.0 atm, the initail volume is 50. In a motorcycle engine, after combustion occurs in the top of the cylinder, the piston is forced down as the mixture of gaseous products undergoes an adiabatic expansion. To find out the final temperature of the gas T f, substitute 292 K for T i, 1.28 for volume expansion ratio V f / V i and 1.40 for γ in the equation T f = T i ( V i / V f ) γ-1 ,įrom the above observation we conclude that, after expansion the final temperature of the gas will be 265 K. Since the gas expand is expanding from its initial volume V i and its initial temperature T i to its final volume V f and its final temperature T f, therefore the equation (1) will be, Where T is the temperature and V is the volume of the gas. The relation between temperature T and volume V from the adiabatic gas equation is, Assuming the process is adiabatic, calculate the final temperature if γ = 1.40 and the volume expansion ratio is 1.28. The gas in a cloud chamber at a temperature of 292 K undergoes a rapid expansion. ![]() The work done for adiabatic compression is given by, On the other hand, if the gas is compressed, the work is done on the gas and is negative. Therefore, heat required to do the work during expansion is,Īs R is gas constant and γ is constant for a given gas, therefore, we find, from equation (3), that work done during an adiabatic expansion is proportional to the fall in temperature. If T 1 and T 2 are the initial and final temperatures of the gas, (b) Analytical MethodĪnalytically, net work W can be calculated by integrating dW between the limits V 1 and V 2. Thus, area occupied below the curve in between AB and CD gives the required value of work done. The net work done to expand the gas from a volume V1 to volume V2 will be, The adiabatic curve PQ for the process is shown in below figure. (i) The container is made up an insulating material. This case is different from the case of isothermal change in two respects. ![]() ![]() For a small expansion of the gas, pressure remains, practically constant, say P. Let the piston of area of cross section ‘A’ move through a small distance dx, so that the gas expands by a small amount dV. Therefore, the energy required for the expansion of the gas is taken from the gas itself so that its temperature falls. Since no heat supplied from outside, adiabatic expansion has occurred. , where Q is the heat, W is the work done and U is the internal energy of the system. If the piston is now moved suddenly outwards, the gas expands, and does some work. Concepts of Physics by HC Verma for JEEĬonsider one gram molecule of a perfect gas, enclosed in a perfectly non-conducting cylinder provided with a non-conducting piston.IIT JEE Coaching For Foundation Classes.
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